二阶非线性特征值问题的正解

Positive Solutions of Nonlinear Second Order Eigenvalue Problems

利用锥不动点指数研究了二阶非线性特征值问题:u″+2ρu=λh(t)f(u),0<t<2π,ρ∈0,12,u(0)=u(2π)≥0,u′(0)=u′(2π)的正解的存在性.

The existence of positive solutions are presented for nonlinear second order eigenvalue problem u″＋ρ^2u=λh（t）f（u）,0〈t〈2π,ρ∈（0,1/2）,u（0）=u（2π）≥0,u′（0）=u′（2π） And the proof uses the theory for fixed point index in the cone.